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Due to the complex narratives often found in historical causes of death, this task has traditionally been manually performed by coding experts. We evaluate the ability of GPT-3.5, GPT-4, and Llama 2 LLMs to accurately assign ICD-10 codes on the HiCaD dataset that contains causes of death recorded in the civil death register entries of 19,361 individuals from Ipswich, Kilmarnock, and the Isle of Skye in the UK between 1861\u20131901. Our findings show that GPT-3.5, GPT-4, and Llama 2 assign the correct code for 69%, 83%, and 40% of causes, respectively. However, we achieve a maximum accuracy of 89% by standard machine learning techniques. All LLMs performed better for causes of death that contained terms still in use today, compared to archaic terms. Also, they performed better for short causes (1\u20132 words) compared to longer causes. LLMs therefore do not currently perform well enough for historical ICD-10 code assignment tasks. 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